Abstract
Let X be an affine toric variety. The total coordinates on X provide a canonical presentation \(\bar X \to X\) of X as a quotient of a vector space \(\bar X\) by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.
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Arzhantsev, I., Bazhov, I. On orbits of the automorphism group on an affine toric variety. centr.eur.j.math. 11, 1713–1724 (2013). https://doi.org/10.2478/s11533-013-0273-1
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DOI: https://doi.org/10.2478/s11533-013-0273-1